Different varieties of shapes differ indigenous each various other in regards to sides or angles. Plenty of shapes have actually 4 sides, but the difference in angle on their sides makes them unique. We speak to these 4-sided forms the quadrilaterals.

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In this article, you will learn:

What a square is.How the different species of quadrilaterals look like.The nature of quadrilaterals.

 

What is a Quadrilateral?

As words suggests, ‘Quad’ means four and also ‘lateral’ way side. Thus a square is a closed two-dimensional polygon comprised of 4-line segments. In an easy words, a square is a form with four sides.

Quadrilaterals space everywhere! from the books, chart papers, computer keys, television, and mobile screens. The perform of real-world instances of quadrilaterals is endless.

Types that Quadrilaterals

There room six quadrilaterals in geometry. Several of the quadrilaterals space surely acquainted to you, if others may not be so familiar.

Let’s take it a look.

RectangleSquaresTrapeziumParallelogramRhombusKite

 A rectangle

A rectangle is a quadrilateral through 4 ideal angles (90°). In a rectangle, both the pairs of the contrary sides are parallel and equal in length.

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Properties that a rhombus

All sides room congruent through definition.The diagonals bisect the angles.The diagonals in a dragon bisect each various other at appropriate angles.

 

Properties of Quadrilaterals

The nature of quadrilateral include:

Every quadrilateral has 4 sides, 4 vertices, and also 4 angles.4The full measure of every the four interior angle of a square is always equal come 360 degrees.The amount of interior angles that a square fits the formula the polygon i.e.

Sum of interior angles = 180 ° * (n – 2), whereby n is equal to the number of sides the the polygon

Rectangles, rhombus, and squares are all types of parallelograms.A square is both a rhombus and a rectangle.The rectangle and also rhombus space not square.A parallel is a trapezium.A trapezium is not a parallelogram.Kite is no a parallelogram.

Classification that quadrilaterals

The quadrilaterals space classified right into two an easy types:

Convex quadrilaterals: These are the quadrilateral with inner angles much less than 180 degrees, and also the two diagonals are inside the quadrilaterals. They encompass trapezium, parallelogram, rhombus, rectangle, square, kite, etc.Concave quadrilaterals: These space the quadrilaterals through at least one internal angle higher than 180 degrees, and also at the very least one that the two diagonals is exterior the quadrilaterals. A dart is a concave quadrilateral.

There is another less common kind of quadrilaterals, called complicated quadrilaterals. These are crossed figures. Because that example, overcome trapezoid, overcome rectangle, overcome square, etc.

Let’s work-related on a few example problems around quadrilaterals.

Example 1

The interior angles of one irregular quadrilateral are; x°, 80°, 2x°, and also 70°. Calculate the value of x.

Solution

By a property of quadrilateral (Sum of internal angles = 360°), we have,

⇒ x° + 80° + 2x° + 70° =360°

Simplify.

⇒ 3x + 150° = 360°

Subtract 150° ~ above both sides.

⇒ 3x + 150° – 150° = 360° – 150°

⇒ 3x = 210°

Divide both sides by 3 to get;

⇒ x = 70°

Therefore, the value of x is 70°

And the angles of the quadrilaterals are; 70°, 80°, 140°, and 70°.

Example 2

The internal angles of a quadrilateral are; 82°, (25x – 2) °, (20x – 1) ° and (25x + 1) °. Uncover the angles of the quadrilateral.

Solution

The total sum of interior angles that in a quadrilateral = 360°

⇒ 82° + (25x – 2) ° + (20x – 1) ° + (25x + 1) ° = 360°

⇒ 82 + 25x – 2 + 20x – 1 + 25x + 1 = 360

Simplify.

⇒ 70x + 80 = 360

Subtract both sides by 80 to get;

⇒ 70x = 280

Divide both sides by 70.

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⇒ x = 4

By substitution,

⇒ (25x – 2) = 98°

⇒ (20x – 1) = 79°

⇒ (25x + 1) = 101°

Therefore, the angle of the square are; 82°, 98°, 79°, and 101°.

Practice Questions

Consider a parallelogram PQRS, whereFind the 4 internal angles of the rhombus whose sides and one of the diagonals space of equal length. 

Answers